[EM] Approximating Non-Summable Methods with Summable Methods

[Abd ul-Rahman Lomax]

Kathy Dopp was replying to Jameson Quinn, in a thread begun with the 
title: [EM] Multiwinner Bucklin - proportional, summable (n^3), 
monotonic (if fully-enough ranked)

Difficult summability creates difficulties with auditing election 
results, which is Kathy's concern. There is a limit to such 
difficulties, because all canvassing methods will work with 
sum-of-ballot-type data, and even if every ballot were unique, then 
the data from each precinct is still transmissible. If such data is 
public, and if raw ballot images (real images!) are provided, the 
public can, and I believe, will audit results such that every ballot 
is redundantly counted and confirmed. That was my Public Ballot 
Imaging concept I put forward some time ago. (Allowing election 
observers to photograph ballots and put up the images obtained. They 
can see them already, why not allow them to share their seeing?)

Short of public ballot imaging, which bypasses the question of who 
watches the watchers, summability remains important.

Bucklin is, of course, easily summable, needing only the totals of 
votes for each candidate divided into the ranks (generally three, 
though a Range ballot could be used with more ranks). The rules would 
need to provide for counting each vote at the highest rank found, and 
then disregarding it if the vote is repeated in the lower ranks. If 
voting machines are used, the multiple votes that would locked out 
would be these additional votes. I.e., the machine would treat each 
candidate as a vote-for-one "race," so that any candidate gets 1st, 
2nd, or 3rd rank, as a choice, with the default, no vote, being the 
fourth rank. Voters are thus separating candidates into two broad 
groups: approved (a vote at some rank) and not-approved (no vote.)

And within the approved rank, voters can pick one of three choices 
for each candidate: Favorite(s), Worst of the Approved, and (Better 
than worst and less than favorite).

It is a very simply system to vote, and bullet voting is quite 
appropriate for many voters, and voting strategy for the rest is 
intuitively simple.

I find it fascinating that what I've come to conclude is the best 
practical voting system, which effectively considers preference 
strength and thus resembles Range Voting (the best theoretical 
system, if somehow we could know absolute utilities and use them), 
was actually invented and used in the United States about a century 
ago! And widely.

And what happened to it is a story that I certainly would like to 
hear. There has been no comprehensive study, it is as if the method 
just vanished. I suspect was that the problem was that it worked, and 
that those who didn't like having a voting system that worked, who 
benefit from the well-known problems of plurality and top-two runoff, 
simply exercised their power. None of this should prevent small 
communities from trying out Bucklin, and the only change appropriate 
now over, say, the Duluth method is that instead of allowing multiple 
voting in third rank only, it should be allowed in all ranks. There 
is no reason to force voters to choose between two candidates that 
the voter considers both excellent, for example. If the voter has 
some preference, the voter is free to vote it without harm. But I 
think the idea that "voting" is about choosing your favorite, 
vote-for-one only, was very strong.

As noted, there are ways to use Bucklin for proportional 
representation, just as there are ways to use Approval, Range, or STV.

Kathy, STV is, of course, IRV, and thus subject to the same 
pathologies, but STV is bitten by these to a much lesser degree 
because of the multiple elections. Absolutely, there are better 
proportional representation methods, the shining star, but still 
untested in public elections, is Asset Voting. (Technically, it can 
be implemented with STV, though I think the complication is 
unnecessary, vote for one actually works fine with Asset.)

The place where voting system science and voting integrity concerns 
meet is in the slogan: Count All the Votes. This means counting, and 
using, "overvotes," in a fair manner. It means counting and reporting 
all votes in an IRV election, not just those needed to determine the 
winner under STV counting rules. And once that is being done, it will 
be seen that IRV pathologies actually do strike in real elections, 
and the fact that IRV can, and does, fail to elect a Condorcet 
winner, instead electing someone who would have lost in a direct 
face-off, will lead to a desire for better methods.

Count All the Votes. Should be start printing bumper stickers? 
Approval Voting/Election Integrity.